Feature selection and feature extraction

Learning machine learning for some time, but even the most basic theoretical problems are not understood, here I briefly explain.

For example, I have a set of L metric values {X1, X2, X3, ... XL};

Feature selection: Select m (m<l) subsets from existing L measures according to a certain standard, {X1, X2, X3, ... Xm}; The M measure is a feature that is reduced to a dimension.

Feature extraction: Make this L measure through some kind of transformation H (*), produce a new M (m<l) subset, {X1, X2, X3, ... Xm}. The new M subset is the feature of descending dimension after feature extraction.

This is illustrated by a popular example:

Example: The difference between feature selection and feature extraction: identification of a bar and a circle.

Solution: [Method 1]
① feature Extraction: Measurement of three structural features
(a) perimeter
(b) Area
(c) Two cross-diameter ratios perpendicular to each other

Analysis: (c) is characterized by its ability to classify, hence the selection (c),
Throw Away (a), (b).

[Method 2]:① Feature Extraction: Measuring the projection of an object to two axes
Value, A and B each have 2 range ranges. It can be seen that the projections of two objects overlap, and the projection values are not used directly The two areas are separated.

② Feature Selection: Rotate the coordinate system in a counterclockwise direction, or the object changes in a clockwise direction, and the appropriate translation and so on. Two objects can be distinguished by the positive or negative values of the coordinates projected on the axis of the object.

Feature selection and feature extraction